A recent paper1 on the quantum mechanical properties of the attractive 1x2 potential explains in simple terms the unusual quantum properties we would expect from a system described by a singular potential. These properties include the need for considering the restrictions imposed by the Hamiltonian H and the renormalization that is required to obtain physically proper (or “true” as they are called in Ref. 1) solutions. Reference 1 also discusses the need to guarantee not only the Hermiticity but also the self-adjointness of H—an operator is self-adjoint if the action of H is the same as that of H and both operators have the same domain, DH=DH. That is, both H and H need to be defined over exactly the same set of functions in Hilbert space.

We will show that the 1...

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